Front

What is an absolute value inequality?

Back

An absolute value inequality is an inequality that contains an absolute value expression, which represents the distance of a number from zero on the number line.

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How do you solve the inequality |x| < a?

Back

To solve |x| < a, you split it into two inequalities: -a < x < a.

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How do you solve the inequality |x| > a?

Back

To solve |x| > a, you split it into two inequalities: x < -a or x > a.

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What does the solution |y - 1| ≤ 6 represent on a number line?

Back

The solution -5 ≤ y ≤ 7 represents all the values of y that are within 6 units of 1 on the number line.

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What does the solution |p + 3| ≥ 10 indicate about p?

Back

The solution p ≤ -13 or p ≥ 7 indicates that p is either less than or equal to -13 or greater than or equal to 7.

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What is the first step in solving an absolute value equation?

Back

The first step is to isolate the absolute value expression on one side of the equation.

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What is the difference between |x| < a and |x| ≤ a?

Back

|x| < a means x is strictly within a units from zero, while |x| ≤ a includes the endpoints, meaning x can be exactly a units from zero.

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What is the difference between |x| > a and |x| ≥ a?

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|x| > a means x is strictly outside a units from zero, while |x| ≥ a includes the endpoints, meaning x can be exactly a units from zero.

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How do you graph the solution of |x| < a?

Back

You graph the interval (-a, a) on the number line, using open circles to indicate that the endpoints are not included.

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How do you graph the solution of |x| > a?

Back

You graph the regions x < -a and x > a on the number line, using open circles to indicate that the endpoints are not included.